Stochastic models of cancer: An update of theory and data

Monday, June 14 at 09:30am (PDT)
Monday, June 14 at 05:30pm (BST)
Tuesday, June 15 01:30am (KST)

SMB2021 SMB2021 Follow Monday (Tuesday) during the "MS01" time block.
Note: this minisymposia has multiple sessions. The second session is MS02-DDMB (click here).

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Marek Kimmel (Rice University, United States), Simon Tavare (Columbia University, United States)


Much has been learned recently about mechanisms of cancer progression, as well as about cancer stochasticity at the molecular and population level, and about interaction of tumors with normal cells of the organism. These developments prompted progress in mathematical, computational and statistical models and tools. This mini-symposium brings together a diverse group of representatives of several leading institutions who will discuss their recent work. Topics range from branching processes and cellular automata, to mathematical models of mutation, genetic drift and selection, immune infiltration of tumors, and evolutionary dynamics of specific types of cancer. They also include statistical methods, such as cancer phylodynamics. The organizers hope these will provide inspiration for further work in the area.

Tibor Antal

(School of Mathematics, Edinburgh University, Scotland, UK, UK)
"Models of Tumor Progression"
I'll review recent results on timing in evolving cell populations. The stochasticity is taken into account by the use of branching processes, and the general question is the time it takes to produce cells with some specific properties. As an application the (possible) relapse time after cancer treatment will be discussed.

Robert Beckman

(Lombardi Comprehensive Cancer Center and Innovation Center for Biomedical Informatics, Georgetown University Medical Center, Washington, DC, USA, USA)
"Recent Advances in Genetic Instability and Dynamic Precision Medicine of Cancer"
Cancer evolution has similarities with species evolution but also important differences. This talk will outline some of these differences, including results from the deepest, most accurate sequencing of a solid tumor done to date. By probing the evolution of extremely rare mutations, we learn that the amount of intratumoral heterogeneity is far greater than previously assumed, and that subclones harboring pre-existing resistance to any single therapy will be universally present in any clinically diagnosable tumor. Moreover, rare mutations evolve neutrally, and surprisingly the popular “infinite sites assumption” suggesting that a new mutation will appear in only one cell at once, does not apply at this stage of tumor growth. Cancer treatment has also evolved, from an empirical science of killing dividing cells, to the current era of “precision medicine”, targeted to molecular features of individual cancers. However, current precision medicine views a single individual’s cancer as largely uniform and static. Moreover, from a strategic perspective, it thinks primarily of the current therapeutic maneuver. In contrast, dynamic precision medicine (DPM) plans ahead, considers intratumoral heterogeneity and evolutionary dynamics, and probabilistically weighs the future benefits of preventing resistance against the benefits of immediate cytoreduction. Simulations indicate it has the potential to double median survival broadly across cancers. This talk will provide background about DPM, highlighting differences from other approaches to evolutionarily directed therapy. It will describe recent advances, including the role of genetically unstable “hypermutator subclones”, the possibility of clinical translation in presurgical “neoadjuvant “ settings, and considerations in clinical trial design.

Alexandre Bouchard-Côté

(Statistics, University of British Columbia, Vancouver, BC, Canada, Canada)
"Inferring fitness of cancer subpopulations from time series --- Bayesian methods for the Wright-Fisher diffusion with selection"
From timeseries of patient-derived xenograft data, we are interested in inferring fitness parameters for sub-populations of cancer cells measured using single cell sequencing. I will describe a statistical model for Bayesian inference of these fitness parameters. The model is based on a stochastic differential equation, the Wright-Fisher diffusion with fitness, the parameters of which are treated as random. We extend advanced MCMC methodologies such as PMCMC to perform Bayesian inference at scale, the posterior distribution being defined over a high-dimensional space and informed by a large dataset.

Ivana Bozic

(Applied Mathematics, University of Washington, Seattle, WA, USA, USA)
"Mathematical model of colorectal cancer initiation"
Cancer evolution cannot be observed directly in patients, and new methodologies are needed for obtaining a quantitative understanding of this obscure process. We developed and analyzed a stochastic model of malignant transformation in the colon that precisely quantifies the process of colorectal carcinogenesis in patients through loss of tumor suppressors APC and TP53 and gain of the KRAS oncogene. Our study employs experimentally measured mutation rates in the colon and growth advantages provided by driver mutations. We calculate the probability of a colorectal malignancy, the sizes of premalignant lesions, and the order of acquisition of driver mutations during colorectal tumor evolution. We demonstrate that the order of driver events in colorectal cancer is determined primarily by the fitness effects that they provide, rather than their mutation rates.

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Virtual conference of the Society for Mathematical Biology, 2021.